Trapezoid TEAM has the following vertices T(-2,3), E(1,0), A(7,6) and M(0,5). Points E, F(h,k) and A are on the same line. If T, E, F and M are the vertices of a square, find h and k.
Hi Magentarita,

Soroban is absolutely right. Perhaps you meant to say rectangle instead of square.

If you're looking to find the coordinates of

**F**, we can procede this way.

The slope of

**TM** = 1. The slope of

**EA = **the slope of

**EF** = 1.

**TM** is parallel to

**EF**.

The slope of

**TE** is -1. Therefore the slope of

**MF **must be -1.

We can now set up a system of equations to solve for

**F(h, k).** [1] [2]
Solving

[1] and

[2],